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 A210877 Triangle of coefficients of polynomials v(n,x) jointly generated with A210876; see the Formula section. 4
 1, 0, 3, 0, 3, 4, 0, 2, 8, 5, 0, 2, 6, 17, 6, 0, 2, 5, 18, 31, 7, 0, 2, 5, 14, 47, 51, 8, 0, 2, 5, 13, 41, 107, 78, 9, 0, 2, 5, 13, 35, 115, 218, 113, 10, 0, 2, 5, 13, 34, 98, 296, 407, 157, 11, 0, 2, 5, 13, 34, 90, 276, 695, 709, 211, 12, 0, 2, 5, 13, 34, 89, 244, 750 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS For n>2, each row begins with 0 and ends with n+1.  If the term in row n and column k is denoted by U(n,k), then U(n,n-2)=A105163(n-1). Row sums: A000225 (-1+2^n) Alternating row sums:  A137470 Limiting row:  0,2,5,13,34,89,..., even-indexed Fibonacci numbers For a discussion and guide to related arrays, see A208510. LINKS FORMULA u(n,x)=x*u(n-1,x)+v(n-1,x)+1, v(n,x)=x*u(n-1,x)+x*v(n-1,x)+x, where u(1,x)=1, v(1,x)=1. EXAMPLE First six rows: 1 1...2 1...1...3 1...1...3...4 1...1...2...8...5 1...1...2...6...17...6 First three polynomials v(n,x): 1, 1 + 2x, 1 + x + 3x^2 MATHEMATICA u[1, x_] := 1; v[1, x_] := 1; z = 14; u[n_, x_] := x*u[n - 1, x] + v[n - 1, x] + 1; v[n_, x_] := x*u[n - 1, x] + x*v[n - 1, x] + x; Table[Expand[u[n, x]], {n, 1, z/2}] Table[Expand[v[n, x]], {n, 1, z/2}] cu = Table[CoefficientList[u[n, x], x], {n, 1, z}]; TableForm[cu] Flatten[%]    (* A210876 *) cv = Table[CoefficientList[v[n, x], x], {n, 1, z}]; TableForm[cv] Flatten[%]    (* A210877 *) Table[u[n, x] /. x -> 1, {n, 1, z}]  (* A000225 *) Table[v[n, x] /. x -> 1, {n, 1, z}]  (* A000225 *) Table[u[n, x] /. x -> -1, {n, 1, z}] (* A077973 *) Table[v[n, x] /. x -> -1, {n, 1, z}] (* A137470 *) CROSSREFS Cf. A210876, A208510. Sequence in context: A210485 A111815 A281269 * A127753 A197736 A073367 Adjacent sequences:  A210874 A210875 A210876 * A210878 A210879 A210880 KEYWORD nonn,tabl AUTHOR Clark Kimberling, Mar 30 2012 STATUS approved

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Last modified May 24 14:49 EDT 2019. Contains 323532 sequences. (Running on oeis4.)